Several recent studies have shown that the anisotropy in the magnetic structure of EuCd₂As₂ plays a significant role in stabilizing the Weyl nodes. To investigate the relationship between magnetic anisotropy and Weyl physics, we present a comparative study between EuZn₂As₂ and EuCd₂As₂ that are isostructural but with different magnetic anisotropy. We performed structural analysis, electronic transport, and magnetization experiments on millimeter-sized single crystals of EuZn₂As₂, and compared the results to those of EuCd₂As₂. By combining the first principle calculations and neutron diffraction experiment, we identify the magnetic ground state of EuZn₂As₂ as A-type antiferromagnetic order with a transition temperature (T_N = 19.6 K) twice that of EuCd₂As₂. Like EuCd₂As₂, the negative magnetoresistance of EuZn₂As₂ is observed after suppressing the resistivity peak at T_N with increasing fields. However, the anisotropy in both transport and magnetization are much reduced in EuZn2As₂. The difference could be ascribed to the weaker spin-orbit coupling, more localized d orbitals, and a larger contribution from the Eu s orbitals in the zinc compound, as suggested by the electronic band calculations. The same band structure effect could be also responsible for the observation of a smaller nonlinear anomalous Hall effect in EuZn₂As₂ compared to EuCd₂As_2.